This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various provinces \(m\) of South Africa. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.
This paper and it’s results should be updated roughly daily and is available online.
As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was b141aff519ee125929b3b6f686b1070f3fc70742.
A major recent update made on 29 March 2021 was to switch from data based on cases reported as captured in [3] to a data source that contains cases by date the specimen was received [4].
A further update on 17 April 2021 was to adjust cases for public holidays and on 18 April 2021 basic testing data was also added.
Case data is extracted from the NICD National COVID-19 Daily Report [4]. This contains the daily cases reported by the NICD for South Africa by province. Data is shown by specimen reported date. Most recent data is excluded due to incomplete reporting of tests in last number of days.
This report contains data as released at 2021-04-23 21:01:06.
The following fixes are applied:
Public holidays tend to have lower number of cases received and results in distortions of the estimation of the reproduction number over time. Below we attempt to adjust for these discrepencies.
Public holiday dates are obtained from [5]
For each province counts of cases is then modelled as a function of:
The impact of public holidays are then removed by observing the impact of public holidays in the model and reversing that out in the data. This has the effect of increasing the observed cases on public holidays and reducing them slightly on all other days. This effect is dependent on the province and day of the week.
The methodology is described in detail here.
Below raw numbers of test by specimen received date are plotted. A 7-day moving average is also plotted. No adjustment is made for public holidays for this data.
Tests
Tests for Last 30 Days
Below raw test positivity by specimen received date is plotted. A 7-day sliding window test positivity rate is also plotted. No adjustment is made for public holidays for this data as both numerator and denominator should be impacted.
Test Positivity
Test Positivity for Last 30-days
Cases before and after adjustment for public holidays for South Africa are shown below for March and April 2021. Cases are increased on days of public holidays and reduced on other days. Weekends are not impacted significantly.
Further in this report the adjusted cases are used.
Unadjusted and Adjusted Daily Cases for South Africa for March & April 2021
Below a 7-day moving average daily case count is plotted by province on a log scale since start of the epidemic:
Daily Cases by Province (7-day moving average)
Below the above chart is repeated for the last 30-days:
Daily Cases for Last 30-days by Province (7-day moving average)
Below current (last weekly) \(R_{t,m}\) estimates are tabulated.
| province | Count (Week) | Week Ending | Reproduction Number [95% Confidence Interval] |
|---|---|---|---|
| Eastern Cape | 157 | 2021-04-19 | 0.8 [0.70 - 0.98] |
| Free State | 1,417 | 2021-04-19 | 1.2 [1.13 - 1.28] |
| Gauteng | 2,229 | 2021-04-19 | 1.0 [0.97 - 1.05] |
| KwaZulu-Natal | 528 | 2021-04-19 | 0.8 [0.76 - 0.91] |
| Limpopo | 150 | 2021-04-19 | 1.0 [0.83 - 1.14] |
| Mpumalanga | 744 | 2021-04-19 | 0.9 [0.87 - 1.01] |
| North West | 974 | 2021-04-19 | 1.1 [1.03 - 1.18] |
| Northern Cape | 897 | 2021-04-19 | 1.3 [1.19 - 1.43] |
| Western Cape | 907 | 2021-04-19 | 1.0 [0.91 - 1.04] |
| South Africa | 8,003 | 2021-04-19 | 1.0 [1.02 - 1.07] |
Estimated Effective Reproduction Number by Province
Below estimates of the reproductive number are plotted on a map of South Africa [6].
Estimated Effective Reproduction Number Based on Cases by Province
Below the results for South Africa over the last 90 days are plotted together with a plot since start of the pandemic.
Estimated Effective Reproduction Number Based on Cases for South Africa over last 90 days
Estimated Effective Reproduction Number Based on Cases for South Africa since 1 April 2020
Below the reproduction number by week by province is animated:
The results for each province over last 90 days are plotted below.
Estimated Effective Reproduction Number Based on Cases for Eastern Cape over Time
Estimated Effective Reproduction Number Based on Cases for Free State over Time
Estimated Effective Reproduction Number Based on Cases for Gauteng over Time
Estimated Effective Reproduction Number Based on Cases for KwaZulu-Natal over Time
Estimated Effective Reproduction Number Based on Cases for Limpopo over Time
Estimated Effective Reproduction Number Based on Cases for Mpumalanga over Time
Estimated Effective Reproduction Number Based on Cases for Northern Cape over Time
Estimated Effective Reproduction Number Based on Cases for Gauteng over Time
Estimated Effective Reproduction Number Based on Cases for Western Cape over Time
Detailed output for all provinces are saved to a comma-separated value file. The file can be found here.
Limitation of this method to estimate \(R_{t,m}\) are noted in [1]:
For example the the generation interval is based on international data and not South African data.
Further to the above the estimates are made under assumption that the cases are detected at a similar ratio to the underlying infections over time. Should this change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of case detection could result in an overestimating recent effective reproduction numbers. A more practical example may be a public holiday resulting in fewer specimens received on a particular day. Or, also, changes in testing, such as using more antigen tests (with lower sensitivity) relative to PCR tests could reduce the case ascertainment rate per test for example.
A relatively simple allowance is made for public holidays so as to avoid volatile figures due to public holidays. This allowance could be refined further but should result in a more consistent estimate of the reproduction number over time. Care should still be taken when reviewing results during periods where testing could be impacted.
Estimates for the reproduction number here are plotted in time period in which the specimen was received. Ideally we would wish to capture the date the infection occurred. These figures have not been shifted back, even approximately, to the date of infection.
Despite these limitation it is believed that the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.
In [7] similar estimate of the reproduction number are made. The main differences from those estimates are:
[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133
[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim
[3] V. Marivate et al., “Coronavirus disease (COVID-19) case data - South Africa.” Zenodo, 21-Mar-2020 [Online]. Available: https://zenodo.org/record/3888499. [Accessed: 26-Oct-2020]
[4] National Institute for Communicable Diseases, “National COVID-19 Daily Report,” 2021 [Online]. Available: https://www.nicd.ac.za/diseases-a-z-index/covid-19/surveillance-reports/national-covid-19-daily-report/
[5] Republic of South Africa, “Public holidays in South Africa.” [Online]. Available: https://www.gov.za/about-sa/public-holidays. [Accessed: 15-Apr-2021]
[6] OCHA, “South africa - subnational administrative boundaries,” Dec. 2018 [Online]. Available: https://data.humdata.org/dataset/south-africa-admin-level-1-boundaries
[7] National Institute for Communicable Diseases, “The Daily COVID-19 Effective Reproductive Number (R) in South Africa,” Week 11 2020 [Online]. Available: https://www.nicd.ac.za/wp-content/uploads/2021/03/COVID-19-Effective-Reproductive-Number-in-South-Africa-week-11.pdf